System for performing spectral analyses under computer control

ABSTRACT

Measurements of physical attributes such as dielectric film thickness that are susceptible to spectral analysis are accomplished rapidly and accurately by a spectrophotometric system in which a programmed digital computer operating concurrently with the optical scanning means automatically performs the calibrating, normalizing and data reducing functions that otherwise must be carried out as time-consuming human, mechanical or analog electronic operations. The control over the optical data handling operations exercised by the computer eliminates the need for mechanically or electronically adjusting the optical apparatus to meet changing system conditions, whether periodic or aperiodic. Source light is transmitted through a rotating variable-wavelength interference filter which acts during one-half of its cycle to transmit light of varying wavelength through a fiber-optic reference path directly to the optical data acquisition apparatus, while acting in the next half-cycle to transmit light of such varying wavelength indirectly to said data acquisition apparatus through a measurement path. In the present example, where film thickness is the attribute being measured, the measurement path comprises a bifurcated fiber-optic bundle, one branch of which is used to carry the light of variable wavelength to the sample, and the other branch of which carries light reflected from the sample to the aforesaid data acquisition apparatus. A computer program enables light passed through the reference path in one half-cyle to calibrate the system for measuring optical transmission or reflectance in the next half-cycle. Reduction of relative reflectance data to absolute reflectance data (needed for the accurate determination of film thickness) is accomplished by additional computer programs whose algorithms are based upon the discovery that all graphs of absolute reflectance versus wavelength for film samples of a given material having different thicknesses are bounded by a common pair of wave envelopes.

llnite States Patent [191 pm et al.

[ Aug. 7, 1973 SYSTEM FOR PERFORMllNG SPECTRAL ANALYSES UNDER COMPUTER CONTROL [75] Inventors: Frederick H. Dill; Karl L. Konnerth,

Jr., both of Putnam Valley, N.Y.

[73 Assignee: International Business Machines Corporation, Armonk, N.Y.

[22] Filed: May 23, 1972 [21] Appl. No.: 256,030

[56] References Cited UNITED STATES PATENTS 3,482,105 12/1969 Hutzler 356/97 X 3,622,765 11/1971 Anderson. 235/1513 3,646,331 2/1972 Lord 235/1513 OTHER PU BLlCATlONS Bey, P. P., Optical Film Tickness Monitoring, In Rev. Sci. Inst. 42(1): p. 57-60, Jan., 1971.

Campbell, R. D., Measurement of Film Thickness, ln Proc. l.R.E.E. Australia, p. 102-104, April, 1967.

Primary Examiner-Malc0lm A. Morrison Assistant Examiner-R. Stephen Dildine, Jr. Att0rney-Charles P. Boberg et al.

[57] ABSTRACT Measurements of physical attributes such as dielectric film thickness that are susceptible to spectral analysis ANALOG are accomplished rapidly and accurately by a spectrophotometric system in which a programmed digital computer operating concurrently with the optical scanning means automatically performs the calibrating, normalizing and data reducing functions that otherwise must be carried out as time-consuming human, mechanical or analog electronic operations. The control over the optical data handling operations exercised by the computer eliminates the need for mechanically or electronically adjusting the optical apparatus to meet changing system conditions, whether periodic or aperiodic. Source light is transmitted through a rotating variable-wavelength interference filter which acts during one-half of its cycle to transmit light of varying wavelength through a fiber-optic reference path directly to the optical data acquisition apparatus, while acting in the next half-cycle to transmit light of such varying wavelength indirectly to said data acquisition apparatus through a measurement path. In the present example, where film thickness is the attribute being measured, the measurement path comprises a bifurcated fiberoptic bundle, one branch of which is used to carry the light of variable wavelength to the sample, and the other branch of which carries light reflected from the sample to the aforesaid data acquisition apparatus. A computer program enables light passed through the reference path in one half-cyle to calibrate the system for measuring optical transmission or reflectance in the next half-cycle. Reduction of relative reflectance data to absolute reflectance data (needed for the accurate determination of fllm thickness) is accomplished by additional computer programs whose algorithms are based upon the discovery that all graphs of absolute reflectance versus wavelength for film samples of a given material having different thicknesses are bounded by a common pair of wave envelopes.

15 Claims, 25 Drawing Figures COMPUTER CONVERTER PHOTO MULTIPLIER Patented Aug. 7, 1973 3,751,643

22 Sheets-Sheet 1 24 ANALDG DIGITAL INTERFACE COMPUTER NON-NORMAL F LIGHT RAYS 22 Sheets-Sheet 2 Patented Aug. 7, 1973 3,751,643

22 Sheets-Sheet 5 WAIT FOR H6 5 600\ sTART COMMAND DATAI 601 ACOUIRE DATA,0VER SELECTED (HGS' 7A 78) 5A sPEcTRAL RANGE, FROM SAMPLE PATH AND REFERENCE PATH FIG. 58 r DIVIDE SAMPLE PATH DATA 602 BYREFERENCE PATH DATA FIG. A

605 IS THIS FIG. 50 MEASUREMENT CAL|B- 0R CALIBRATION? 604 FIG. 606 5E DIVIDE DATA BY ACTUAL DIVIDE DATA BY CALIBRATION REFLECTANCE FACTORS To OBTAIN RELATIVE 0F CALIBRATING REFLECTANCE DATA SAMPLE THIKI 60? A 605 (ms 8MP) MAKE ROUGH EUSTIMATEMOF STORERESUUS J NUMBER OF FRINGES m A T REFLECTANCE CURVE AS FACTORS 7 FIG. 5A USE THIS NUMBER To A DETERMINE HOW MANY 608 DATA POINTS TD M m CALCULATIONS SMOOTHING OF DATA DESIRED YES SMOOTH DATA WITH ONE OF VARIOUS STANDARD TECHNIQUES Patented Aug. 7, 1973 3,751,643

22 Sheets-Sheet 4 FIG. 5 B

NOTATE DATA POINTS AS BAD IF INCREIIENTAL (ADJACENT POINTS) DERIVATIVE CHANGES SIGN AT 6II THAT POINT AND THEN REVERTS TO PREVIOUS SIGN AT NEXT POINT NOTATE AS BAD ANY DATA POINTS TAKEN AT VIAVELENGTHS WHERE FILN IS HIGHLY ABSORBINC (FOR EXAMPLE THE BLUE END OF SPECTRUM THTH PHOTORESIST) FIND MULTIPLIER REQUIRED TO FIT REFLECTANCE CURVE BETWEEN ENVELOPE CURVES AND WAVE LENGTHS /6I5 AT WHICH POINTS OF TANGENCY OCCUR (IFANY; IF NONE MULTIPLIER CANNOT BE DETERMINED) IVERE ANY POINTS OF TANGENCY FOUND THINI (FIGS. IOA & IOB) WHAT IS SIGN OF SLOPE 0F REFLECTANCE POSITIVE ORDR 9H0) HoTATE POINTS 0T TANGENCY FOR ORDER CHANGE INFORMATION /6I5 IN CALCULATIONS VERY THIN FILM;

NEGATIVE USE CURVE FITTING TEcHHTouE To GET e19 APPROXIMATE THICKNESS DETERMINE MULTIPLIER BY I CALCULATING IT AT WHICIIEVER 617 END OF CURVE IS CLOSEST TO BEING A POINT OF TANGENCY TO ENVELOPE Patented Aug. 7, 1973 3,751,643

22 Sheets-Sheet 5 NOTATE l NCREMENTAL SLOPE AT ORDR EAON POINT FOR PROPER SIGN 61 (CONT-D) OETERNTNATTON 0F ARC COSINE 8 EVALUATION IN LATER CALCULATIONS m FILM NO ABSORPTION BE NEOLEOTEO e22 MULTIPLY REFLECTANCE CURVE HT CURVE To Poms 0F TANOENOT 0F UPPER ENVELOPE BY MULTIPLIER FOUND ABOVE TO OBTAIN ABSOLUTE REFLECTANCE FOR BEST APPROX'W'W T0 ABSOLUTE REFLECTANCE ESTIMATE FRINGE OROER 625 AT ONE END OF cuRvE CALCULATE FILM THICKNESS AT EAON GOOD USED WAVELENGTH USING sTANOARO FORMULAS ANO 2 CHANGING OROER AT EAON POINT OF TANGENCY TO UPPER ENVELOPE TNTNT (CONT'D) CALCULATE ANO TEMPORA'R ILY sAvE AvERAOE 0F THICKNESSES CALCULATED /625 ANO THEIR sTAN DARD DEVIATION Fl G. 56 626 IS THIS TNE YES FIRST PASS THROUGH THIS SECTION Patented Aug. 7, 1973 3,751,643

22 Sheets-Sheet 6 IS STANDARD DEVIATION CALCULATED THIS TIME LARGER THAN FOR 62T LAST PASS INCREMENT STARTING ORDER GUESS THICKNESS CALCULATED TIME I BEFORE THIS PASS IS 629 CORRECT RESULT IS REFINEMENT ITERATION TO BE USED PRINT ANSWER THIKI (CONT'D) RESET ORDER INFORMATION TO VALUE FOR CORRECT /652 ANSWER ABOVE DECREASE MULTIPLIER BY 655 SOME REASONABLE AMOUNT (E.C.20%)

CALCULATE NEW REFLECTANCE 634 BY MULTIPLYINC ORIGINAL CURVE BY NEW MULTIPLIER Patented Aug. 7, 1973 CALCULATE FILM TH ICKNESS AT EACH WAVELENGTH USI NG CORRECT ORDER VALUES TH IKI (CONT'D) I FIG. 5E

22.5heets-Sheet 7 CALCULATE AND TEII PORARILY SAVE AVERAGE OF THICKNESSES AND "STANDARD DEVIATION IS THIS THIS SECTION IS STANDARD LAST PASS FIRST PASS THROUGH DEVIATIDN CALCULATED THIS TI IIE LARGER THAN FOR YES INCREIIENT MULTI PLIER BY REASON AB LE AMOUNT (EC/1% I THICKNESS CALCULATED TIME BEFORE THIS PASS 7 IS CORRECT RESULT PRINT RESULT FIG. 6

22 Sheets-Sheet 8 &0 1

LOWER wAvE ENVELOPE WAVELENGTH (A) Patented Aug. 7, 1973 FIG. 7A

DATAI INT BEGIN LOOP].

AGAIN EXIT STATS XRl XRZ CONT 22 Sheets-Sheet 9 SUBROUTINE DATAI THIS ROUTINE IS USED TO AQUIRE DATA WHERE THE PROGRAM HAS 3 WAITS /3OFO WAITING FOR START PULSE /3OF1 W ITING FOR A/D CONV COMPLETE /3OFZ WAITING FOR END PULSE TO CHECK FOR A VALID SET OF DATA DATAI I. NORMAL ENTRY BEGIN INTERRUPT ENTRY POINT SENSE DSW SAVE DSW FOR END CHECK INT RI' 'I SAVE XRl ST TS SAVE STATUS DATAI PUT POINTER IN XRl DATAI 93 UPDATE RETURN ADDRESS 0 LOAD N (NUMBER OF SETS) SETS AND STORE IN SETS I LOAD M (NUMBER OF POINTS) NPNTS AND STORE IN NRNTS 2 LOAD STARTING ADDR OF IDAT STADT AND STORE IN STADT LOC AND IN LOC 16 ZERO ACCUMULATOR NPNTS LOAD XRZ FOR COUNTING LOC ZERO IDATA LOCn'l I DECREMENT COUNTER LOOP]. LOOP IF MORE 20 LOAD XRI WITH LIMI TING NUMBER OF RUNS I DECREMENT LI MIT COUNTER CONT CONTINUE IF NOT EXCEEDED DABLB IF EXCEEDED n DISABLE HFFFF INTERRUPTS AND LOAD ACC 16 AND EXT WITH ONES /3OFF THEN WAIT I BOFFI DABLB DISABLE BOTH INTERRUPTS RESTORE STATUS RESTORE XRl RESTORE XRZ DATAI RETURN NPNTS LOAD XRZ FOR COUNT ING-STORING Patented Aug. 7, 1973 FIG. 7B

LOOPZ LOOP3 DABLB NABLB SENSE NABLS NABLT READ START TWORD DBOTH NBOTH HFFFF DSW LOC RDNO NPNTS STADT SETS DATA XIO XIO DC XIO LD STO MDX XIO LD BNN LD STO LDX LD A STO 22 Sheets-Sheet l0 NABLS /3OFO NABLT /3OF1 READ RDNG DATA "1 LOOPZ NABLB /30F2 DSW AGAIN STADT LOC NPNTS DATA LOC LOC LOCo-I ""1 1.0093 SETSvI AGAIN EXIT DBOTH /99OO NBOTH /99OO NABL WAIT NABL WAIT INT FROM START PULSE FOR START INT A/D INT 0 DABLE START OR A/D CONV COMP INT READ Patented Aug. 7, 1973 22 Sheets-Sheet 11 FIG.8A

SUBRDUTINE THIKI I.I00.0.00...OOOOIIIIOD'IIIOIIOOOOOOOIIIO.IOIIOIIOUIOIIOIIOOIIQC'O THIS SUBROUTINE RETURNS A MEASURED FILM THICKNESS VALUE THIS VERSION HAS THE OPTION FOR ITERATING ON AMXMNo .0ll CIIOIOIII'OQOOOQ'QIIC'O'.I.IO'OIOQOIIIII' IOIOIQ'IO'Q'I...

SUBROUTINE THIKI (AAVGQSDEV) DIMENSION REFU 5b) oMDERISA) OMORDRID) QIBAD(54) aRFMAXIS H DIMENSION EDATA(205) 9 IDATAI360) DIMENSION GOOD( 54) QTHICKI 54) OFLMAXIZO) 0FRMAX(ZO) COMMON CALIM 54) sCOEFI'HBO) a COEFLIIOO) CAL-AMS) QSIGMAI54) COMMON RlR2S( 54) oTURl2(54) 1R1SZS(54) uFMAXl54) 'FMIN 54-) oAMULTI54) COMMON INC, INCFvINCLo-NMBRvMGOa ISWO: ISHl 'ISWZv [SW30 ISWHISWB COMMON ISW6aISW7aISWB QISW90 ISWlOo ISWII' ISWlZoISWlk EQUIVALENCE(EDATA( 1 s28 ;RFMAX(1 OTHICKI 1] EOUIVALENCEIEDATAI 1 91 OREFL I 1) EOUIVALENCEI IDATM 1 oGOODII QFLMAXI 1 e I IDATAUvl) ,FRMAX( 1) EOUIV LENCH IDATAI 109) QMDER(1) I o I IDATA(163) uMORDRI l) EQUIVALENCEI IDATAIZIT) IBADU.) EQUIVALENCEIEDCMXuAMAXuAVGPDnSUMaDEVl EQUIVALENCEIEDCMNoAMINaAVGMDoAMXMN) I EDDMNAVGI INITIALIZE VARIOUS QUANTITI E5 IORCH Z ACQUIRE DATA CHECK ISWI To SEE IF EVERY 1 OR 3 DEGREE MODE TO BE USED GO TO (25015) 0 ISWl DATA POINT EVERY THREE DEGREES OF ROTATION CALL OATAI (H IZOIIDATA) EDATAI 101 I 'IDATAI I+63)/40 EDATAIZQI I IDATAI I+3)/4n GO TO 35 DATA POINT EVERY DEGREE OF ROTATION BUT USING ONLY THE 54 POINTS AT THE RED END OF THE SPECTRUM (FOR THICK FILMS) CALL DATAI (4036O0IDATA) DO 30 I I. 054

EDATAI 1 9X )'IDATA( I+296 l n EDATAIZ I )=IDATA( I+116) l u CALCULATE CALIBRATION AND DATA MAXIMA AND MINIMA Patented Aug. 7, 1973 22 Sheets-Sheet 12 FIG. 88

IF (EDATA(2, I) EDCMX) 43,43,42 EDCMX-EDATA(2,I) IF (EDATA(2,I)EDCMN) 44,45, 15 EDCMN=EDATA(2 I) IF (EDATA(1, I)-EDDMX) 47,47,46 EDDMX=EDATA(1 ,1) IF (EDATA(1, I)-EDDMN) 48 ,50, 5O

EDDMN=EDATA(1,I) CONTINUE WRITE MESSAGE IF SIGNAL TOO LARGE OR TOO SMALL IF( EDCMN-GO. 5 0 051 051 IFIEDDMN-BC- 54052052 IFIEDCMX-AO70. I 53053055 IFl EDDMX-ADTO. I 5666.55 WRITE 1 504) EDCMNQEDDMN GO TO 52 WRITE I 1 I506) EDCMXsEDDMX RETURN TYPE CALIBRATION AND DATA MAXIMA AND MINIMA IF ISWZ I GO TO (57058) 0 ISWZ WRITEI 1 I501) EDCMX !EDCMN9EDDMX0E DDMN IF ISWO 1' DATA IS TREATED AS A CALIBRATION ON BARE SILICON AND THE CALIBRATION FACTORS C MPUTED AND STORED ON DISK AND THEN RETURN IS MADE TO CALLING PROGRAM GO TO (59,65 I a ISWD DO 60 B105 C LIBI I I-(EDATAIZ. I )/EDATA( l; I 'FMAXI I I GO TD (64:62] u ISWI.

WRITEI l '3) CALIB WRITEI105OB) RETURN WRITEI 1 '4) CALIB VIRITEI I 509) RETURN IF ISWO 2o DATA IS TREATED AS A MEASUREMENT AND THE REFLECTIVITY I5 CALCULATED DO I=l n54 REFLI I I I EDATA(20I IEDATA l o I I I /CALIB( I I MAKE A ROUGH ESTIMATE OF THE NUMBER OF MAXIMA IN THE REFLECTIVITY CURVE AND FROM THIS DECIDE HOW MANY DATA POINTS SHOULD BE USED AND IF THE SMOOTHING ROUTINE SHOULD BE USED Patented Aug. 7, 1973 22 Sheets-Sheet 14 TO TOP CURVE ONLY. IF(MGO1) 143,177,143 IF (KRMAX) 177 ,177 ,145

CALL LSQZ (FLMAX,FRMAX,KRMAX,CO,C1,C2

DO 150 I=l,54

REFL (I)=REFL (I)/ (CO+Cl*ALM(I)+ALM(I) AMXMN=1.

MAKE SURE THERE AREN'T SO MANY BAD POINTS THAT THE DATA IS USELESS OR THE NORMAL ROUTINE IF THERE ARE TRY THE THIN ROUTINE IF THERE IS NO MAXIMUM OR MINIMUM IN THE DATA AND WE ARE NOT IN THE 1300 ANGSTROM REGION THEN GO TO TH IN ROUTINE GO TO (285 9300) vJGO WRITE 1 1503) CALL THI NI (REFL oAAVGsAMXMN) IF AAVGI 2879287 9290 IF THE THIN ROUTINE DOES NOT GIVE A POSITIVE ANSWER a URI TE MESSAGE SET ANSWER TO ZERO AND RETURN WRI TE( 1 9530) AAVG=OI RETURN CHECK TO SEE WHETHER MULTIPLIER ADJUSTMENT IS TO BE USED 60 TO (291 0289) nISWlA DELTAIOOE*AMXMN NORDRzl SDEV IuEB IBRCH=1 DO 297 I INCQFJAIINC MDERI I )=1 IF THE DATA LOOKS OK CALCULATE THE ARCCOS TERM IN THE EQUATION FOR THE THICKNESS AND THE FIRST CALCULATION OF THICKNESS DO 310 I=INCF IINCLQINC IF( IBAD( I 1 30703070310 COSIN: (REF+REF*RIRZS I 1"RI$2S( I I (REF-10 )*TUR12( I I 1 IF I CQSIN-Iu I 3019301 0302 I F(COSIN+10 I 3039304430 ANGLE=OO GO TO 305 ANGLE 314159265 Patented Aug. 7, 1973 22 Sheets-Sheet 15 GO TO 306 ANGLE=ACOS(COSINI IF(MDER( I T T 30603060305 ANGLE-ANGLE THICM I (ANGLE+(MORDR( IHNORDR-l '6aZ63l85314-SIGPUH I) AMULT I CONTINUE CALCULATE THE THICKNESS AT ALL GOOD POINTS FOR THE PRESENT STA TING ORDER (NORDRh AVERAGE THESE AND CALCULATE STANDARD DEVIATION KOUNT=O SUM-O0 DO 410 I'INCF0INCL0INC THICTU I )THICIU I )+6oZ831B531*AMULT( I 7 IF( IBAD( I I I 005 0405 0 010 KOUNT KOUNT+1 GOODMOUNTI THICKI I I SUM SUM+THICKI I I CONTINUE AVG'SUM/KOUNT DO 020 I-10KOUNT X'GOOD! 1 )-AVG DEV'DEV4-X'X DEV'SORT (DEV/KOUNT) BRANCH DEPENDENT UPON WHETHER ITERATION IS TO BE DONE ON NORDR OR AMXMN GO TO 0520 025) 0 IBRCH COMPARE STD DEV TO THAT FROM PREVIOUS ATTEMPT (OR TO INITIAL STD DEV VALUE OF 10E36 IF FIRST ATTEMPT) 0 IF NEH VALUE IS SMALLER THAN 0LD0 INCREMENT NORDR AND TRY AGAIN. IF LARGERo SETTLE FOR THIS RESULT IF(DEV-SDEV) 02904340 034 NORDR NORDR I IF NO SOLUTION IS FOUND TO ORDER 000 TYPE MESSAGE AND RETURN IF(NORDR- 0O) +01 0 001 0 031 WRITEI l 0505) GO TO 288 IF STD DEV GETS TOO LARGE0 TRY THE THIN ROUTINE IF( BOOc-SDEV) 03504360436 WRITE! 10507) AAVG0SDEV GO TO 266 BRANCH DEPENDENT UPON WHETHER AMXMN ITERATION IS NOW TO BE USED 60 TO 0380289) 0ISW1 0 Patented Aug. 7, 1973 22 Sheets-Sheet 16 IF SO: SET UP FOR THE ITERATION G DELTA=-O45*AMXMN NOROR=NORDR-l IBRCH l GO TO 300 REGION IN WHICH TESTING IS DONE FOR AMXMN ITERATION IF DEV-'SDEV) AAAVG=AAVG SSDEV=SDEV AAVG=AVG SDEV=DEV I F(AMXMN-2u 5504559457 AMXMN=AMXMN-DELTA GO TO 300 WRITE! l 0530) GO TO 288 453 abl i461 CALL. PRAB(AAAVGoAAVGyAVGoSSDEVaSDEVsDEVoXaY) AAVG=X GO TO 289 FORMAT MFlOoZ/ FORMAT NO MAX/MIN--TRY THIN FORMAT 'PMT OUT LO aZFlO-O) FOR AT( NO SOLN FOUND--RSLT SET=0 FORMAT( 'PMT OUT TOO HI u2Fl0.0)

FORMAT 'SCATTER TOO LRG-TRY THIN QZFIOQO) FORMAT( END MOD 3 CAL FORMAT END 1 DEGREE CAL ORMAT( NO MEANINGFUL SOLN--RSLT SETO' FORMAT TOO MANY BAD PNTS-TRY THIN 7 END Patented Aug. 7, 1973 3,751,643

22 Sheets-$heet 18 so CONTINUE wsmmcnwsmvmo JDERHNCHJDERIZINCI NOTATE BAD POINTS OF RFMAX AND RFMIN IN 15w AND JBAD, RESP.

O DENOTES GOOD AND 1 DENOTES BAD (MEANING THAT THE DERIVATIVE HAS CHANGED SIGN 3 TIMES BETWEEN A USED DATA POINTS) DO 70 I= INCFy INCL, INC I INC= I-INC I INC=I+INC IF( IDERI I I-IDER( IMINC I I 61 062 '61 IF( IDER I I I-IDERI IPINC I I 63 162,63

IBADI I I=O GO TO 64 IBAD( I I =1 IDER( I I=ICERI IMINCI I F I JDER( I I'-JDER( IMINC 65 o6665 I F( JDERI I I-JDER( IPINCI I 67 66,67

JBAD( I I I JDERI I I JDER( IMINCI CONTINUE IF ANY OF ISHB THRU ISWIO II 1 INDICATING PHOTORESIST MEASUREMENT AND ISWI 2 I INDICAT ING MEASUREMENT UNDER ABOUT 20 I000 ANGSTROMSI I .E. 0 EVERY 3 DEGREES USED ON FILTER) NOTATE THE F IRST I2 DATA OINTS AS BAD DUE T LARGE ABSORPTION IN THAT REGION 60 TO (225 0210) ISWI DO 220 I=l 912 IBADI I I=l KBADI I I =1 INITIALIZE VARIOUS PARAMETERS CONT=NUMBER OF POINTS OF TANGENCY TO ENVELOPE CURVES D IV$ -"'USED TO WEIGH POINTS OF TANGENCY TO TOP ENVELOPE CURVE MORE HEAVI LY THAN TO BOTTOM FOR NUMEROUS REASONS A AX ACCUMULATED WEIGHTED MULT I PLYING FACTORS KR AX=NLJMBER OF OINTS OF TANGENC TO TOP ENVELOPE CURVE USED FOR PHOTORESIST CALCULATIONS THIS IS 7 FRMAX i I I=RFMAX AT TANGENCY POINTS TO TOP ENVELOPE A FLMAX( I I=WAVELENGTH AT TANGENCY POINTS TO TOP ENVELOPE J L G=INDI CATOR AS TO WHETHER LAST POINT OF TANGENCY HAS TO TOP ENVELOPE CURVE (0 I BOTTOM (l I OR NOT KNOWN (-l) MCONT=O DIVSR O. AMAXOQ KRMAX=O JFLAG="1 FIND POINTS OF TANGENCY TO ENVELOPE CURVES I IF ANY I BY FINDING Patented Aug. 7, 1973 22 Sheets-Sheet l9 REL TIVE MAXIMA OF RFMAX AND RELATIVE MINIMA OF RFMIN. NEGLECTING POINTS NOTATED AS BAD IN IBAD OR JBAD AND UNDER THE C NSTRAINTS THAT THE POINTS OF TANGENCY MUST ALTERNATE BETWEEN TH ENVELOPE CURVES AND THAT THEY MUST BE WITHIN A SPECIFIED FACTOR OF THE ABSOLUTE OF RFMAX AND RFMIN (TO AVOID TREATING NOISE NEAR A MINIMA AS A MAXIMA ETC- a A PARABOLIC FIT IS DONE TO THE 3 POINTS NEAREST THE TANGENCY POINTS. THE MIDDLE POINT OF THESE 3 IS NOTATED AS BAD IN KBAD) TO AVOID CALCULATI G WHICH SIDE F TANGENCY POINT IT IS ON. FIRST AND LAST POINTS ALSO NOTATED A5 BAD SINCE ORDER CANNOT BE EASILY DETERMINED FOR THEM ORDER CHANGES (POINTS OF TOP TANGENCY) ARE NOTATED IN MORDR TRUE LOCAL INCREMENTAL DERIVATIVE OF ACTUAL CURVE NOTATED IN KDER FOR LATER USE IN DETERMINING THE PROPER SIGN OF ARCCOS DO 100 I=INCFo INCLQINC IMINC= I-INC I F( IBAD( I T T 71971085 IF RFMAX( I )-l.5*RFMXN) 85 972 972 IF(RFMAX I I )-RFMAX( IMINC) 85.74.74 IF(RFMAX I )-RFMAX( IPINC) 55076.76 IF(JFLAG) 78998u78 JFLAG=O MCONT=MCONT+I KRMAX=KRMAX+1 CALL PRABIALAMI IMINC) QALAMI I QALAMI IPINC) 'RFMAXI IMINC) :RFMAX( I |RF *MAX IPINC) ,XoY)

FRMAX(KRMAXI==Y FLMAX KRMAX I I F( JBAD( I I 86086099 IF( RFMIN I )-65*RFMNXI 87 087.99

IF(RFMIN( I )-RFMIN( IPINC) I 92992099 I (R MIN( I J-RFMINI IMINC) 88 y88999 I F( JFLAG) 94094098 JFLAG=1 MCONT=MCONT+1 DIVSR=DIVSR+1.

CALL PRAB(ALAM( IMINC) vALAM( I IALAMI IPINC) RFMIN( IMINC) 0RFMIN( I I QRF *MIN I IPINC) vXoY) AMAX=AMAX+Y KBADI I l MORDR( I )=-KRMAX KDER( I )=JFLAG I CONTINUE KBADI INC i l KDER( INC)=K DER( INCF KDER(54)=(DER( INCL) MORDR! INC) MORDRI INCF) MORDR(54) MORDRI INCL) FIG. 9C

MAKE STARTING ESTIMATE OF ORDER AT SHORT WAVELENGTH END OF CURVE 

1. A method of operating a spectrophotometric system under the control of a digital computer to determine an attribute of a given material sample which is subject to spectral analysis, said method comprising the steps of: a. conducting to said sample, during each of a series of nonadjacent time periods, a beam of variable wavelength monochromatic light furnished by a given source, the wavelength of said beam varying at a given rate through a specified range of wavelength values during each of said periods; b. conducting to a light detector in said system the light which comes from said sample when it is impinged by said beam; c. conducting directly to said light detector, during time periods intervening the periods specified in step a, the beam of monochromatic light furnished by said source, the wavelength of which varies at said given rate through said specified range during each of said intervening periods; d. converting the output of said detector during each of the periods specified in steps a and c to a sequence of stored digital values representing the respective intensities of light detected at a series of regularly timed intervals throughout the respective one of said periods; e. operating said computer to derive from the sequences of values stored during any pair of successive steps a and c a new sequence of numbers representing the calculated optical responses of said sample to incident light having the wavelength of said variable-wavelength beam at each of said timed intervals under a hypothetical condition where it is assumed that the incideNt light has uniform intensity for all wavelengths in said range and all system components have constant operating characteristics; and f. operating said computer to determine from said derived sequence of numbers the attribute of said sample which is being measured.
 2. A method of operating a spectrophotometric system under the control of a digital computer to determine the thickness of a film of given dielectric material, said method comprising the steps of: a. conducting to said film, during each of a series of nonadjacent time periods, a beam of variable-wavelength monochromatic light furnished by a given source, the wavelength of said beam varying at a given rate through a specified range of wavelength values during each of said periods; b. conducting to a light detector in said system the light reflected from said film as it is illuminated by said beam; c. conducting directly to said light detector, during time periods intervening the periods specified in step a, the beam of monochromatic light furnished by said source, the wavelength of which varies at said given rate through said specified range of values during each of said intervening periods; d. operating said computer to convert the output of said detector during each of the periods specified in steps a and c to a sequence of stored digital values representing the respective intensities of light detected at a series of regularly timed intervals throughout the respective one of said periods; e. operating said computer to derive from the sequences of digital values stored during any pair of successive steps a and c, as described above, a series of numbers each representing the relative reflectance of said film when illuminated by monochromatic light having the wavelength of said beam at a respective one of said timed intervals under a hypothetical condition where it is assumed that the incident light has uniform intensity for all wavelengths in said range and all system components have constant operating characteristics; and f. operating said computer to determine from said relative reflectance values the thickness of the film being measured.
 3. In a spectrophotometric system having data acquisition means for generating digital value-representing signals in response to sensed optical inputs and also having a digital computer provided with data storage means and data processing means which are responsive to the output of said data acquisition means, a method of operating said system to measure the thickness of a film sample of given dielectric material, comprising the steps of: a. conducting to said film sample, during each of a series of nonadjacent time periods, a beam of variable-wavelength monochromatic light furnished by a given source, the wavelength of said beam varying at a given rate through a specified range of wavelength values during each of said periods; b. conducting to a light-sensitive input device in said data acquisition means the light which is reflected from said sample when it is impinged by said beam; c. conducting directly to said light-sensitive device, without impinging said sample and during time periods intervening those specified in step a, the beam of variable-wavelength monochromatic light furnished by said source, the wavelength of which varies at said given rate through said specified range of values during each of said intervening periods; d. operating said computer to receive and store in said data storage means, at regularly timed intervals in each of the time periods described in a and c, the digital values generated by said data acquisition means, thereby to store at least two sets of numbers, one set representing the respective intensities of light detected by said light-sensitive device at said timed intervals during a period when the variable-wavelength light beam is being conducted directly to said device, and the other set of numbers representing the respective intensities of light detected by said device at said timed intervals during a period when the variable-wavelength light beam is impinging said film sample; e. storing in said data storage means a set of numbers representing the respective wavelengths of the light beam at the respective ones of said timed intervals throughout any of said periods; f. operating said data processing means to derive from all of the stored number sets recited hereinabove a table of values representing the manner in which the relative reflectance of said film sample varies with respect to the wavelength of the incident light beam under a hypothetical condition where it is assumed that the incident light has uniform intensity for all wavelengths in said range and all system components have constant operating characteristics; g. operating said data processing means to multiply the relative reflectance values in said table by a factor which will convert the curve of relative reflectance versus wavelength to a curve which is at least approximately tangent to predefined upper and lower wave envelopes that bound the curves of absolute reflectance versus wavelength for all films of the given material having thicknesses within a predetermined thickness range; and h. operating said data processing means to compute from the multiplied reflectance values the thickness of said film sample.
 4. A computer-controlled spectrophotometric system for measuring a property of a given material sample which is subject to spectral analysis, said system comprising: a. cyclically operable illuminating means for furnishing a beam of monochromatic light, the wavelength of which varies periodically at a given rate through a specified range of wavelength values; b. a light detector; c. first light guiding means for conducting said light beam through a first path directly to said light detector during nonadjacent ones of the periods in which the wavelength of said light beam undergoes variation through said range of values; d. second light guiding means effective during periods intervening said nonadjacent periods for conducting said light beam through a second path having an initial portion that directs said beam to said sample and a final portion that conducts light from said sample to said detector; e. signal converting and data transfer means responsive to the output of said detector and operating in a timed relationship with the cyclic operation of said illuminating means for producing sequences of digital value representations, each such sequence denoting the variation of detected light intensity with respect to the wavelengths of said beam at a series of regularly timed intervals within each of said periods; and f. a digital computer having data storage means for storing the sequences of digital value representations produced by said means e during at least two successive periods when said detector is receiving light through said first path and said second path, respectively, and having data processing means to calculate from such stored data the optical responses which would have been obtained from said sample at said timed intervals if the conditions had been such that the intensity of the variable-wavelength incident light were uniform at all wavelengths in said range and the operating characteristics of the components of said system were constant, thereby providing a new set of corrected values from which the measurement of said sample property can be accurately determined.
 5. A spectrophotometric system as set forth in claim 4 wherein said illuminating means a comprises the following elements: a1. a source of polychromatic light; a2. first light conducting means for directing polychromatic light from said source to an exit point optically aligned with but spaced from the entrance to said first path in said first light guiding means; a3. second light conducting means for directing polychromatic light from said source to an exit point oPtically aligned with but spaced from the entrance to said second path in said second light guiding means; and a4. a rotatable variable-wavelength interference filter positioned so that it rotates alternately past the entrance to said first path and the entrance to said second path, the wavelength of the monochromatic light transmitted by said filter to either path depending upon the angular position of said filter.
 6. A spectrophotometric system as set forth in claim 5 wherein each of said light conducting means and light guiding means is a fiber-optic bundle.
 7. A system as set forth in claim 6 wherein said second light guiding means (d) is a bifurcated fiber-optic bundle, one branch of which constitutes said initial portion, and the other branch of which constitutes said final portion.
 8. A spectrophotometric system as set forth in claim 4 which includes timing means under the control of said illuminating means for causing said signal converting and data transfer means to sample the output of said light detector at predetermined wavelength increments during each of the periodic variations of the monochromatic beam wavelength.
 9. A spectrophotometric system as set forth in claim 4 wherein said computer is programmed to divide each of the values in the sequence that was received through said second path by the correspondingly positioned value in the sequence that was received through said first path.
 10. A spectrophotometric system as set forth in claim 4 wherein said second light guiding means is arranged so that light passed through said initial portion thereof is reflected from said sample and passed through said final portion thereof to said detector.
 11. A system as set forth in claim 10 wherein said computer is programmed to divide each of the values in the sequence that was received through said second path by the correspondingly positioned value in the sequence that was received through said first path, thereby to yield said sequence of corrected values representing the relative reflectance of said sample at the respective wavelengths assumed by said beam at said timed intervals.
 12. A system as set forth in claim 11 wherein said computer is programmed to multiply each of the values in said relative reflectance sequence by a factor which will cause the multiplied values to define a curve that is tangent to at least one of a pair of predetermined wave envelope curves which bound all curves of absolute reflectance versus wavelength for the given material, thereby providing a set of absolute reflectance values for said respective wavelengths.
 13. A system as set forth in claim 12 wherein said computer is programmed to calculate from said sequence of absolute reflectance values the thickness of said sample.
 14. In a computer-controlled spectrophotometric system of the kind wherein a light detector is arranged to respond to light of periodically varying wavelength which is received alternately through a sample measurement path and a direct reference path, the combination comprising: a. a rotatable variable-wavelength filter having a light-transmitting portion with an angular span not exceeding 180* positioned so that it transmits light into the respective entrances of said measurement path and said reference path during different periods in its rotation, the wavelength of the light transmitted into either of said paths at any instant depending upon the angular position of said filter relative to the path entrance; b. a polychromatic light source; and c. means providing light conducting paths leading from said light source to exits on the side of said filter which is farthest from said measurement path and reference path entrances, said path exits being respectively aligned optically with said entrances, whereby the rotation of said filter causes polychromatic light emerging from said path exits to be transmitted by said filter as monochromatic light of varying wavelength to said measurement path and said reference path, respectively, during different periods in the rotation of said filter.
 15. The combination set forth in claim 14 wherein said means c is a split fiber-optic bundle having branches leading respectively to said exits and having a common portion adjacent to said light source wherein the fibers of said branches have a randomized distribution. 